%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET643+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:14:52 PM UTC 2026
% Result : Theorem 0.15s 0.66s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 176 ( 68 ~; 67 |; 13 &)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 2 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(prove_relset_1_5,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_5) ).
fof(c_0_7,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p15]) ).
fof(c_0_8,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p13]) ).
fof(c_0_9,plain,
! [X33,X34] :
( ( ~ ilf_type(X33,set_type)
| empty(X33)
| member(esk6_1(X33),X33) )
& ( ~ ilf_type(X33,set_type)
| empty(X33)
| ilf_type(esk6_1(X33),set_type) )
& ( ~ ilf_type(X33,set_type)
| ~ member(X34,X33)
| ~ ilf_type(X34,set_type)
| ~ empty(X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).
fof(c_0_10,plain,
! [X8] : ilf_type(X8,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_11,plain,
! [X26,X27] :
( ( ~ ilf_type(X26,set_type)
| ~ ilf_type(X27,set_type)
| ilf_type(X27,subset_type(X26))
| ~ ilf_type(X27,member_type(power_set(X26))) )
& ( ~ ilf_type(X26,set_type)
| ~ ilf_type(X27,set_type)
| ilf_type(X27,member_type(power_set(X26)))
| ~ ilf_type(X27,subset_type(X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
fof(c_0_12,plain,
! [X36,X37] :
( ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X37,set_type)
| empty(X37)
| ilf_type(X36,member_type(X37))
| ~ member(X36,X37) )
& ( ~ ilf_type(X36,set_type)
| ~ ilf_type(X37,set_type)
| empty(X37)
| member(X36,X37)
| ~ ilf_type(X36,member_type(X37)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_13,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X40,X41,X42] :
( ( ~ ilf_type(X40,set_type)
| ~ ilf_type(X41,set_type)
| member(X40,power_set(X41))
| ~ member(esk8_2(X40,X41),X41) )
& ( ~ ilf_type(X40,set_type)
| ~ ilf_type(X41,set_type)
| member(X40,power_set(X41))
| member(esk8_2(X40,X41),X40) )
& ( ~ ilf_type(X40,set_type)
| ~ ilf_type(X41,set_type)
| member(X40,power_set(X41))
| ilf_type(esk8_2(X40,X41),set_type) )
& ( ~ ilf_type(X40,set_type)
| ~ ilf_type(X41,set_type)
| member(X42,X41)
| ~ member(X42,X40)
| ~ ilf_type(X42,set_type)
| ~ member(X40,power_set(X41)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p11])])])])])]) ).
cnf(c_0_16,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2)
| empty(X2)
| ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14])]) ).
cnf(c_0_19,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk8_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X1,power_set(X2))
| member(esk8_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X12,X13,X14,X15] :
( ( ~ ilf_type(X12,set_type)
| ~ ilf_type(X13,set_type)
| ilf_type(X15,subset_type(cross_product(X12,X13)))
| ~ ilf_type(X15,relation_type(X12,X13)) )
& ( ~ ilf_type(X12,set_type)
| ~ ilf_type(X13,set_type)
| ilf_type(X14,relation_type(X12,X13))
| ~ ilf_type(X14,subset_type(cross_product(X12,X13))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])])]) ).
cnf(c_0_22,plain,
( ~ ilf_type(X1,member_type(power_set(X2)))
| ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_14])]) ).
cnf(c_0_23,plain,
( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_14]),c_0_14])]),c_0_18]) ).
cnf(c_0_24,plain,
( ~ member(esk8_2(X1,X2),X2)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_14]),c_0_14])]) ).
cnf(c_0_25,plain,
( member(X1,power_set(X2))
| member(esk8_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_14]),c_0_14])]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_5]) ).
cnf(c_0_27,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( ~ member(X1,power_set(X2))
| ilf_type(X1,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,negated_conjecture,
( ~ ilf_type(cross_product(esk1_0,esk2_0),relation_type(esk1_0,esk2_0))
& ilf_type(esk2_0,set_type)
& ilf_type(esk1_0,set_type) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_14]),c_0_14])]) ).
cnf(c_0_32,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
~ ilf_type(cross_product(esk1_0,esk2_0),relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET643+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.57 % Computer : n002.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 05:33:48 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.62 Running first-order theorem proving
% 0.15/0.62 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.66 % Version: 3.5.1
% 0.15/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.66 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.66 % Starting sh5l with 300s (1) cores
% 0.15/0.66 % new_bool_3 with pid 2528464 completed with status 0
% 0.15/0.66 % Result found by new_bool_3
% 0.15/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.66 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.15/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.66 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.66 % SubtermCWHack with pid 2528467 completed with status 0
% 0.15/0.66 % Result found by SubtermCWHack
% 0.15/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.66 % Search class: FGHSF-FFMF21-SFFFFFNN
% 0.15/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.66 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.66 % Preprocessing time : 0.003 s
% 0.15/0.66
% 0.15/0.66 % Proof found!
% 0.15/0.66 % SZS status Theorem
% 0.15/0.66 % SZS output start CNFRefutation
% See solution above
% 0.15/0.66 % Parsed axioms : 20
% 0.15/0.66 % Removed by relevancy pruning/SinE : 2
% 0.15/0.66 % Initial clauses : 37
% 0.15/0.66 % Removed in clause preprocessing : 0
% 0.15/0.66 % Initial clauses in saturation : 37
% 0.15/0.66 % Processed clauses : 70
% 0.15/0.66 % ...of these trivial : 8
% 0.15/0.66 % ...subsumed : 8
% 0.15/0.66 % ...remaining for further processing : 54
% 0.15/0.66 % Other redundant clauses eliminated : 0
% 0.15/0.66 % Clauses deleted for lack of memory : 0
% 0.15/0.66 % Backward-subsumed : 0
% 0.15/0.66 % Backward-rewritten : 3
% 0.15/0.66 % Generated clauses : 56
% 0.15/0.66 % ...of the previous two non-redundant : 44
% 0.15/0.66 % ...aggressively subsumed : 0
% 0.15/0.66 % Contextual simplify-reflections : 1
% 0.15/0.66 % Paramodulations : 56
% 0.15/0.66 % Factorizations : 0
% 0.15/0.66 % NegExts : 0
% 0.15/0.66 % Equation resolutions : 0
% 0.15/0.66 % Disequality decompositions : 0
% 0.15/0.66 % Total rewrite steps : 67
% 0.15/0.66 % ...of those cached : 49
% 0.15/0.66 % Propositional unsat checks : 0
% 0.15/0.66 % Propositional check models : 0
% 0.15/0.66 % Propositional check unsatisfiable : 0
% 0.15/0.66 % Propositional clauses : 0
% 0.15/0.66 % Propositional clauses after purity: 0
% 0.15/0.66 % Propositional unsat core size : 0
% 0.15/0.66 % Propositional preprocessing time : 0.000
% 0.15/0.66 % Propositional encoding time : 0.000
% 0.15/0.66 % Propositional solver time : 0.000
% 0.15/0.66 % Success case prop preproc time : 0.000
% 0.15/0.66 % Success case prop encoding time : 0.000
% 0.15/0.66 % Success case prop solver time : 0.000
% 0.15/0.66 % Current number of processed clauses : 51
% 0.15/0.66 % Positive orientable unit clauses : 14
% 0.15/0.66 % Positive unorientable unit clauses: 0
% 0.15/0.66 % Negative unit clauses : 1
% 0.15/0.66 % Non-unit-clauses : 36
% 0.15/0.66 % Current number of unprocessed clauses: 11
% 0.15/0.66 % ...number of literals in the above : 29
% 0.15/0.66 % Current number of archived formulas : 0
% 0.15/0.66 % Current number of archived clauses : 3
% 0.15/0.66 % Clause-clause subsumption calls (NU) : 80
% 0.15/0.66 % Rec. Clause-clause subsumption calls : 76
% 0.15/0.66 % Non-unit clause-clause subsumptions : 6
% 0.15/0.66 % Unit Clause-clause subsumption calls : 39
% 0.15/0.66 % Rewrite failures with RHS unbound : 0
% 0.15/0.66 % BW rewrite match attempts : 15
% 0.15/0.66 % BW rewrite match successes : 3
% 0.15/0.66 % Condensation attempts : 0
% 0.15/0.66 % Condensation successes : 0
% 0.15/0.66 % Termbank termtop insertions : 4228
% 0.15/0.66 % Search garbage collected termcells : 833
% 0.15/0.66
% 0.15/0.66 % -------------------------------------------------
% 0.15/0.66 % User time : 0.013 s
% 0.15/0.66 % System time : 0.003 s
% 0.15/0.66 % Total time : 0.016 s
% 0.15/0.66 % Maximum resident set size: 3656 pages
% 0.15/0.66
% 0.15/0.66 % -------------------------------------------------
% 0.15/0.66 % User time : 0.018 s
% 0.15/0.66 % System time : 0.008 s
% 0.15/0.66 % Total time : 0.026 s
% 0.15/0.66 % Maximum resident set size: 4608 pages
% 0.15/0.66 % E exiting
%------------------------------------------------------------------------------